The present invention relates to a bundle of optical fibers used as optical sensors for measuring the displacement of an edge of a body having the form of a sheet or belt and the width of the body, or detecting an image of the body.
As shown in FIG. 1, in a conventional method (U.S. Pat. No. 3,089,484) of measuring with a high dimensional accuracy the running characteristic of a body having a long strip shape such as a magnetic tape, light rays emitted from a light source 1 are changed by a lens 2 into parallel rays to pass through a single optical fiber 3 for producing incident light, the incident light is received by and passes through a single optical fiber 4, to be converted into a voltage by a photoconductive element 6 and an electric circuit (not shown), and thus the displacement or movement of a strip-shaped body 5 interposed between the optical fibers 3 and 4, that is, placed in an aperture portion of such a sensor can be detected. FIG. 2a shows the light receiving surface of the optical fiber 4 having a circular cross section and a coordinate system. Now, let us express the radius of the optical fiber, the displacement of the body 5 at the aperture portion of the sensor, and the light output of the sensor corresponding to the displacement by R.sub.o, X, and Y, respectively. When the light incident upon the optical fiber 4 is uniformly received by the photoconductive element 6 without any loss, the light output Y in a range of displacement -R.sub.o .ltoreq.X.ltoreq.R.sub.o is given by the following formula: ##EQU1##
By performing the above-mentioned integral calculation, the light output Y is expressed as follows: ##EQU2##
Accordingly, when the value of the radius R.sub.o is taken as 1, a relation between the displacement X and light output Y such as shown in FIG. 2b is obtained. It is known from FIG. 2b that the light output varies non-linearly with the displacement. That is, the conventional method has a problem that a non-linear relation exists between the displacement of a measured body and the light output of the sensor.